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Delft University of Technology

1. Steverink, Lisa (author). Secure spectral clustering: The approximation of eigenvectors in the integer domain.

Degree: 2017, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:284fc7f2-440d-4435-ae04-fea83d12c12f

In this thesis, the adaptation of the spectral clustering algorithm to the privacy preserving domain was investigated. The spectral clustering algorithm divides data points into clusters according to a measure of connectivity. A pivotal part of spectral clustering is the partial eigendecomposition of the graph Laplacian. Two numerical algorithms are used to approximate the eigenvectors of the Laplacian: the Lanczos algorithm and the QR algorithm. These numerical methods are adapted to work on Paillier encrypted data values. The main challenge is the fact that Paillier encryption can only be applied to a field of positive integers. Moreover, cryptographic protocols have to be invoked to perform non-linear operations. Also, the square root and division operations are computationally heavy in the privacy preserving domain. The numerical algorithms are adapted to overcome these challenges and be more suitable to work on encrypted values.

Applied Mathematics

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APA (6^{th} Edition):

Steverink, L. (. (2017). Secure spectral clustering: The approximation of eigenvectors in the integer domain. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:284fc7f2-440d-4435-ae04-fea83d12c12f

Chicago Manual of Style (16^{th} Edition):

Steverink, Lisa (author). “Secure spectral clustering: The approximation of eigenvectors in the integer domain.” 2017. Masters Thesis, Delft University of Technology. Accessed January 26, 2021. http://resolver.tudelft.nl/uuid:284fc7f2-440d-4435-ae04-fea83d12c12f.

MLA Handbook (7^{th} Edition):

Steverink, Lisa (author). “Secure spectral clustering: The approximation of eigenvectors in the integer domain.” 2017. Web. 26 Jan 2021.

Vancouver:

Steverink L(. Secure spectral clustering: The approximation of eigenvectors in the integer domain. [Internet] [Masters thesis]. Delft University of Technology; 2017. [cited 2021 Jan 26]. Available from: http://resolver.tudelft.nl/uuid:284fc7f2-440d-4435-ae04-fea83d12c12f.

Council of Science Editors:

Steverink L(. Secure spectral clustering: The approximation of eigenvectors in the integer domain. [Masters Thesis]. Delft University of Technology; 2017. Available from: http://resolver.tudelft.nl/uuid:284fc7f2-440d-4435-ae04-fea83d12c12f